exciton dynamics in monolayer transition metal dichalcogenides

Research Article Journal of the Optical Society of America B 1

Exciton Dynamics in Monolayer Transition MetalDichalcogenidesGALAN MOODY1,†, JOHN SCHAIBLEY2, AND XIAODONG XU2,3,*

1National Institute of Standards & Technology, 325 Broadway, Boulder, CO 803052Department of Physics, University of Washington, Seattle, Washington 981953Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195†Corresponding author: [email protected]*Corresponding author: [email protected]

Compiled March 15, 2016

Since the discovery of semiconducting monolayer transition metal dichalcogenides, a variety of experi-mental and theoretical studies have been carried out seeking to understand the intrinsic exciton popula-tion recombination and valley relaxation dynamics. Reports of the exciton decay time range from hun-dreds of femtoseconds to ten nanoseconds, while the valley depolarization time can exceed one nanosec-ond. At present, however, a consensus on the microscopic mechanisms governing exciton radiative andnon-radiative recombination is lacking. The strong exciton oscillator strength resulting in up to ∼ 20%absorption for a single monolayer points to ultrafast radiative recombination. However, the low quantumyield and large variance in the reported lifetimes suggest that non-radiative Auger-type processes obscurethe intrinsic exciton radiative lifetime. In either case, the electron-hole exchange interaction plays an im-portant role in the exciton spin and valley dynamics. In this article, we review the experiments and theorythat have led to these conclusions and comment on future experiments that could complement our currentunderstanding. © 2016 Optical Society of America

OCIS codes: (160.6000) Semiconductor materials; (300.6470) Spectroscopy, semiconductors; (320.7130) Ultrafast processes incondensed matter, including semiconductors.

http://dx.doi.org/10.1364/ao.XX.XXXXXX

1. INTRODUCTION

Two-dimensional materials such as graphene, black phospho-rous, and transition metal dichalcogenides (TMDs) exhibit fas-cinating physical properties stemming from their unique bandstructure and reduced dimensionality [1]. In recent years, TMDs(MX2, where M = Mo, W and X = S, Se) in particular haveattracted significant interest as a novel testbed of exciton many-body physics of 2D systems [2], while providing an excellentplatform for ultrathin optoelectronic and photonic devices [3].Similar to graphene, monolayer TMDs are composed of a two-dimensional honeycomb lattice (Fig. 1(a)) and can be isolatedthrough mechanical exfoliation or grown using chemical vapordeposition and physical vapor transport techniques. As thematerial thickness is reduced to a single monolayer, TMDs tran-sition from an indirect bandgap semiconductor to one with adirect gap at the two inequivalent K and K′ momentum valleyslocated at the edges of the Brillouin zone, resulting in a thousand-fold increase in optical emission at visible wavelengths (Fig. 1(b))[4, 5].

The unique combination of time-reversal symmetry, broken

inversion symmetry, and strong spin-orbit splitting in mono-layer TMDs leads to coupled spin and valley physics [6, 7]. Atthe conduction and valence band edges, the orientation of theelectronic spin is locked with the valley pseudospin degree offreedom, resulting in chiral optical selection rules: band-edge op-tical transitions at the K valley are coupled to σ+ polarized lightat normal incidence, while transitions in the K′ valley couple toσ− polarized light (Fig. 1(c)).

The optical spectra of monolayer TMDs feature pronouncedpeaks associated with exciton-type transitions, which inherit thechiral optical selection rules [8–10]. The large electron and holeeffective masses arising from the atomic d-orbitals, combinedwith reduced dielectric screening in two dimensional systems,leads to exceptionally strong Coulomb interactions and corre-lations between the charge carriers. Electron-hole pairs formtightly bound excitons with a ∼ 1 nm Bohr radius and a ∼ 500meV binding energy–over an order of magnitude larger thanconventional semiconductors [11–18]. Through electrostatic gat-ing, the exciton charge state can be modified, as illustrated inthe photoluminescence intensity map in Fig. 2(a) [19], which

http://dx.doi.org/10.1364/ao.XX.XXXXXX


features neutral and charged excitons (trions) [20–22]. Theseexcitonic states exhibit rich many-body interaction effects, suchas excitonic molecules (biexcitons) [23–25] and strong couplingbetween excitons and trions [26–28].

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Fig. 1. (a) Schematic illustration of the two-dimensional hexag-onal lattice formed from {Mo, W} and {S, Se} atoms. Opti-cal band gaps form at the K and K′ valleys on the edge of theBrillouin zone. (b) Photoluminescence spectrum for mono-layer (ML) and bilayer (BL) WSe2. (c) Sketch of the valley-dependent optical selection rules near the band edges. Theelectronic spin states are labeled by the arrows, shown forWX2. In the K (K′) valley, the optically active transition cou-ples to σ+ (σ−) polarized light at normal incidence.

The robust optical selection rules for the exciton and triontransitions are illustrated by the steady-state photoluminescencespectrum in Fig. 2(b). After optical excitation of excitons in the Kvalley using σ+ polarized light, emission primarily occurs fromexcitons in the same valley, indicating a high degree of valley po-larization, defined as ρc = (I+ − I−) / (I+ + I−), where I+ (I−)is the σ+ (σ−) polarized emission intensity (or horizontally (H)and vertically (V) polarized emission for linear excitation anddetection). As the photo-excitation energy is increased furtherabove the band edge, intervalley carrier scattering occurs witha higher probability and the degree of polarization decreasesas shown in Fig 2(c). Alternatively, one can excite the excitontransitions using linearly polarized light, shown in the photo-luminescence spectra in Fig. 2(d). The σ+ and σ− componentsof the linearly polarized pump photons excite charge carriers inboth the K and K′ valleys. The electronic wavefunctions evolvewith a fixed relative phase relationship during the hot-carrier re-laxation, exciton formation, and emission processes. As a result,

the emitted photons at the exciton energy are linearly polarizedprimarily along the pump photon polarization direction–a sig-nature of optically induced valley coherence [17, 19]. Valleycoherence is sensitive to the electronic wavefunction overlapand band alignment, which can be modified by an electrostaticfield in gated samples (Fig. 2(e)).

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Fig. 2. (a) Photoluminescence intensity map of exfoliatedmonolayer WSe2 as a function of electrostatic gate voltage andphoton emission energy showing exciton (X), negative trion(T−) and its fine structure (T∗−), and positive trion (T+) transi-tions. (b) Polarization-resolved photoluminescence spectrumat +10 V gate voltage for σ+ (black curve) and σ− (red curve)detection. The incident laser is σ+ polarized. (c) The degree ofexciton and trion polarization decreases with increasing pumpphoto-excitation energy. (d) Polarization-resolved photolumi-nescence spectrum at +10 V gate voltage for horizontally (H,black curve) and vertically (V, red curve) polarized detection.The incident laser is horizontally polarized. (e) The degree ofexciton linear polarization as a function of gate voltage. Datareproduced from [19].

The high degree of valley polarization and valley coherenceoffers novel opportunities for manipulating the valley pseu-dospin degree of freedom. In order to leverage these uniquephysical properties of TMDs for valleytronic and optoelectronicapplications, however, a clear understanding of the exciton ra-diative and non-radiative recombination, valley polarization,and valley coherence dynamics is required. One can get a senseof the relative weight of radiative and non-radiative recombi-


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Fig. 3. Schematic illustration of the prevalent exciton radiative and non-radiative recombination processes in monolayer TMDs.The conduction and valence bands are labeled with the electronic spin orientations, shown in this case for WX2. The filled andempty symbols represent an electron and hole, respectively. Radiative recombination can occur through the exciton transition(a). Alternatively, the exciton can bind with a free carrier to form a trion (b) or with another exciton to form a biexciton state (c),which subsequently emit photons red-shifted by the trion and biexciton binding energy, respectively. (d) Inter-valley scattering ofeither the electron or hole (or both) can occur. Only the case in which both the electron and hole scatter to a spin state with invertedorientation in the K′ valley results in an optically active bright exciton. (e) The center-of-mass momentum and phase of a brightexciton can be altered through intra-valley scattering of the electron and/or hole (left panel). A bright exciton becomes opticallydark via a spin flip of the constituent electron (right panel). Non-radiative recombination can also occur through (f) interbandexciton-exciton Auger scattering, (g) defect-assisted carrier-carrier Auger scattering, and (h) defect-assisted exciton-exciton Augerscattering.

nation by measuring the absolute quantum yield–that is, bycomparing the number of photons emitted from the monolayerto the number of photo-excited excitons. As-grown monolayershave exhibited poor luminescence absolute quantum yield rang-ing from < 0.1% to 6%, implying that ultrafast non-radiativedecay channels compete with and can even dominate radiativerecombination [4, 29].

In order to gain a deeper understanding of the processesgoverning the recombination dynamics, time-resolved photolu-minescence and ultrafast nonlinear optical spectroscopy tech-niques have been implemented. The exciton population decaydynamics typically exhibit multiple exponential componentswith time constants ranging from hundreds of femtoseconds[30, 31] to ten nanoseconds [32]. At present, however, a consen-sus on the microscopic origins of the fast and slow time constantsis still lacking. On the one hand, the strong exciton oscillatorstrength, resulting in up to ∼ 20% optical absorption for theexciton transition in a single monolayer [33], implies efficientradiative recombination. Calculations of the radiative lifetimefor excitons with zero center-of-mass momentum predict a sub-picosecond radiative decay [31, 34]. On the other hand, the lowquantum yield and large variance in the reported populationlifetimes point towards a strong influence on the recombinationdynamics from surface states, impurities, defects, and excita-tion conditions [32, 35]. In the following sections, we reviewthe experimental and theoretical findings that have led to theseconclusions and discuss possible experiments to enhance ourunderstanding of exciton recombination dynamics in monolayerTMDs.

2. POPULATION RECOMBINATION DYNAMICS

Connecting the exciton decay dynamics to radiative and non-radiative processes can be ambiguous in time-resolved spec-troscopy experiments due to the presence of defect and impuritystates, which often appear in steady-state photoluminescencespectra as broad peaks red-shifted from the exciton resonance by∼ 100 meV (see Fig. 2). Interpretation of the exciton dynamicsand comparison between different studies is also complicatedby the presence of low-lying dark exciton states and bright edgestates on the micron-sized monolayer flakes [36, 37]. These statesprovide additional relaxation channels for charge carriers andmay or may not contribute to exciton recombination dependingon the excitation conditions and sample preparation. Such ascenario has stimulated numerous studies aiming to unambigu-ously separate intrinsic exciton radiative recombination fromnon-radiative decay processes.

The prevalent radiative and non-radiative relaxation channelsin monolayer TMDs are illustrated by the energy diagrams inFig. 3. The lowest (highest) energy conduction (valence) bandstates at the K/K′ valleys are identified and labeled with thecorresponding electronic spin orientation, shown in this case forWX2. The spin polarization of electrons in the lowest energyconduction band are expected to be opposite to that of holesin the upper valence band, in contrast to MoX2 [38]. In themajority of spectroscopy experiments, which use non-resonantoptical excitation, hot carriers are excited high in the bands andthen cool on a sub-picosecond timescale followed by excitonformation. The exciton-bound electron and hole can radiativelyand non-radiatively recombine to give rise to multi-exponential


decay dynamics.

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Fig. 4. (a) Temperature dependence of the photoluminescencedecay dynamics of the lowest-energy exciton resonance inmonolayer MoS2 exfoliated onto a 300-nm-thick SiO2/Si sub-strate. The sample is excited using a 532 nm laser. The timetraces are offset vertically for clarity. (b) Above 150 K, a long-lived exponential decay component appears with a time con-stant that increases with temperature. (c) The amplitude of thelong-lived component increases monotonically with tempera-ture. Data reproduced from [39].

The majority of time-resolved spectroscopy experiments haverevealed two or three exponential decay time constants character-izing the recombination dynamics. Using time-resolved photo-luminescence spectroscopy, Korn et al. measure a biexponentialresponse, shown in Fig. 4(a) for monolayer MoS2 exfoliated onto300-nm thick SiO2 on a silicon substrate [39]. Below 150 K, theexponential population dynamics exhibit a single exponentialresponse with a decay time that is resolution-limited at 5 ps.Above 150 K, a long-lived component appears with a decay timeincreasing up to 100 ps at 270 K (Fig. 4(b)). The amplitude of thelong-lived component also increases monotonically with temper-ature (Fig. 4(c)). This behavior is attributed to exciton-phononintra-valley coupling of carriers to higher momentum states (leftpanel in Fig. 3(e)), which changes the exciton center-of-massmomentum by scattering it to an optically inactive dark state out-side of the light-cone, i.e. the region in momentum space withinwhich the emission of a photon can occur while energy andmomentum conservation laws are obeyed. After scattering outof the light cone, the exciton center-of-mass momentum must bereduced through additional scattering events before the excitoncan radiatively recombine. At elevated temperatures, exciton-phonon scattering occurs with a higher probability, resultingin a larger amplitude and slower decay time of the long-livedcomponent.

First-principles calculations of the intrinsic exciton radia-tive lifetime lend additional credence to this interpretation.Palummo et al. combine density functional theory (DFT) andthe GW-Bethe Salpeter equation method to compute the exci-tonic band structure, absorption spectrum, and wavefunction inmonolayer TMDs [34]. Using Fermi’s Golden rule, the radiativelifetime of excitons with zero center-of-mass momentum andat zero temperature is predicted to range from 190 fs to 240 fs

depending on the constituent M and X atoms. Sub-picosecondradiative recombination has been reported in a recent ultrafastoptical-pump and THz-probe spectroscopy study of monolayerWSe2 [30]. In this work, Poellmann et al. measure a 150 fs life-time component, which is attributed to radiative recombinationof bright excitons within the light cone with near-zero center-of-mass momentum. A rate equation analysis taking into accountboth bright and dark exciton transitions yields consistent resultsbetween the fast radiative decay of low-momentum excitonsand the overall low quantum yield from their sample (∼ 10%).

In the majority of ultrafast spectroscopy experiments, how-ever, the average response of a thermal distribution of excitons inmomentum space is probed. Excitons are expected to thermalizeon a timescale comparable to the radiative lifetime, which canbe attributed to inelastic exciton-phonon scattering processesthat change the in-plane exciton momentum [40]. A thermal-ized distribution of excitons can be described using Boltzmannstatistics according to N = exp(−Ek/kbT), where Ek is the exci-ton energy, kB is the Boltzmann constant, and T is the sampletemperature. When considering radiative recombination, the re-sponse of the distribution of excitons must be taken into account,leading to an effective radiative lifetime. Palummo et al. predictthat the effective lifetime increases linearly with temperature ata rate of ∼ 1− 10 ps/K and ranges from 1-10 ps at 4 K to 1-5 nsat room temperature [34]. These values are comparable to thelow-temperature lifetime and linear increase with temperaturereported by Korn et al. shown in Fig. 4(b), although an order-of-magnitude discrepancy exists at room temperature. A fast 4.5ps (≤ 3 ps) exciton lifetime at 4 K is also reported in exfoliatedMoS2 (MoSe2) using time-resolved photoluminescence [41, 42].At elevated temperatures, tri-exponential exciton recombina-tion dynamics have been identified in suspended MoS2 usingtransient absorption spectroscopy [40]. Shi et al. report time con-stants of 2 ps, 75 ps, and 850 ps; the long time component is inexcellent agreement with the above calculations for an averagethermalized distribution of excitons at room temperature.

At cryogenic temperatures, ultrafast quenching of excitonemission on a sub-picosecond to few-picosecond timescale hasbeen attributed to several competing factors in addition to ra-diative recombination. The fast and intermediate lifetimes mea-sured by Shi et al. might be related to the presence of defects,impurities, edge states, and substrate effects, discussed in moredetail below. Additionally, low-lying optically dark excitonstates can influence the fast and slow recombination dynamics[34, 43]. Emission from the optically bright exciton transitioncan be quenched on a picosecond timescale through inter- andintra-valley scattering and spin flip of the electron to form a darkexciton, illustrated by the processes in Fig. 3(d) and the rightpanel of Fig. 3(e) [44–46]. At elevated temperatures comparableto or larger than the conduction band splitting, both the brightstate and low-lying dark state are occupied according to Boltz-mann statistics. Zhang et al. provide evidence that both excitonstates are populated in exfoliated WSe2 above 80 K, resulting ina long lifetime component attributed to both fast non-radiativerecombination and slower radiative recombination on the orderof one nanosecond [43]. However, below 80 K, a thermal equilib-rium is not established between these states, and the dark statesserve as a fast non-radiative relaxation channel that competeswith radiative recombination on a ∼ 10 ps timescale (limited bythe instrument response function in this particular study) [43];however, the nature of and characteristic timescale for bright-to-dark state conversion is likely sensitive to the material compo-sition. For example, the inverted spin polarization and smaller


conduction band splitting in MoX2 compared to WX2 (2-3 meVcompared to tens of meV, respectively) may result in a thermalequilibrium between bright and dark states even at cryogenictemperatures, potentially eliminating this contribution to thequenching of exciton emission in MoSe2 and MoS2.

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Fig. 5. Room temperature differential reflectance spectroscopyof monolayer WSe2 exfoliated onto a silicon substrate with a280-nm thick SiO2 layer. The differential reflection dynamicsmeasured using a 750 nm probe and 405 nm pump are shownin (a) for pump fluence increasing from 0.11 to 1.66 µJ/cm2

(bottom to top). Inset: signal dynamics at early probe delays.(b) The long-lived exciton lifetime component (blue circles,left axis) and the signal intensity (red circles, right axis) as afunction of pump fluence. Data reproduced from [47].

The ultrafast recombination dynamics have also been at-tributed to exciton and carrier Auger-type processes. The two-dimensional nature of TMDs and the heavy effective masses ofthe carriers enhance the Coulomb interactions and correlationsbetween charge carriers, which results in exceptionally strongexciton-exciton and carrier-carrier scattering in these materials[48]. Scattering between two excitons can induce non-radiativeinterband recombination of one exciton and subsequent scatter-ing of the other, conserving energy and momentum as illustratedin Fig. 3(f). Exciton-exciton annihilation has been verified ex-perimentally through exciton density dependent measurementsof the recombination dynamics at room temperature in exfoli-ated MoS2, measured using ultrafast transient absorption spec-troscopy [49]. Through a rate equation analysis that includes adecay channel varying quadratically with the exciton density,Sun et al. extract an exciton-exciton annihilation rate of 0.04

cm2/s, implying an effective exciton lifetime of ∼ 10 ps at anexciton density of 1012 cm−2 (exciton-exciton separation of 10nm). At comparable excitation densities in MoSe2, an order-of-magnitude larger exciton-exciton annihilation rate of 0.33 cm2/sis reported [50]. At these exciton densities, biexciton formationalso provides an efficient relaxation channel with a quadraticdependence of the signal on the pump fluence [23, 25].

In the low-density regime (≤ 1012 cm−2), extrinsic factors caninfluence exciton recombination dynamics and can even domi-nate over exciton-exciton interband annihilation. It is reasonableto speculate that the two-dimensional nature of atomically thinTMDs leads to a strong influence on the optical and electronicproperties from point defects such as M and X vacancies, in-terstitial sites, impurity atoms, and grain boundaries [51, 52].Impurity atoms can introduce free carriers into the system, re-sulting in non-radiative decay of the bright exciton populationthrough an exciton-to-trion conversion process via charge-carriercapture by the exciton on a picosecond timescale (Fig. 3(b)) [27].

Defect and impurity states also serve as a center for efficientnon-radiative recombination provided the final state wavefunc-tion strongly overlaps with the Bloch states of the valence andconduction bands. In a simple picture, an electron (hole) canscatter off a hole (electron), consequently being captured intoa defect or impurity state while the hole (electron) scatters to ahigher energy state to conserve energy, as illustrated in Fig. 3(g).The capture time into defect states via carrier-carrier Auger scat-tering is predicted to vary from 0.5-3 ps and is independent ofthe pump fluence for exciton densities ranging from 1011 − 1012

cm−2 [48]. At excitation densities ≥ 1012 cm−2, a combinationof linear and quadratic pump fluence dependence of the carriercapture rates into defect states is expected; in contrast to exciton-exciton interband annihilation, this nonlinear behavior arisesfrom the capture of an electron or hole from one exciton andconcurrent scattering of a hole or electron in the other (see Fig.3(h)). While the former does not require the presence of defectand impurity states, the probability of the latter increases as thedefect energy within the bandgap approaches the conduction(valence) band for electron (hole) capture [48].

Density independent Auger scattering may be reflected inthe room-temperature differential reflectance spectra shown inFig. 5, measured from monolayer WSe2 exfoliated onto a 280-nm thick SiO2 layer on a silicon substrate [47]. In this study,Cui et al. report a constant ∼ 18 ps exciton lifetime for exci-tation densities up to 1011 cm−2, which is consistent with thedensity-independent carrier capture rates predicted by Wanget al. [47, 48]. The short exciton lifetime in Fig. 5(b) is alsotentatively attributed to phase-space filling, Coulomb screen-ing, and bandgap renormalization effects. Mouri et al. reportsimilar results for WSe2 on quartz for exciton densities near1011 cm−2; however, as the density is further decreased to 109

cm−2, the lifetime increases to ∼ 4 ns, which suggests minimalcontributions from defect-assisted non-radiative recombinationin this study. This highly nonlinear behavior is attributed todiffusion-assisted exciton-exciton annihilation at a rate of 0.35cm2/s and a diffusion length up to 1.8 µm [53]. The large vari-ation in reported annihilation rates and exciton lifetimes for agiven excitation density might be attributed to a strong influencefrom the substrate. For example, the exciton-exciton annihilationrate decreases by more than a factor of two when transferringfrom a supported substrate to a suspended monolayer in WS2and MoS2, which can significantly affect the quantum yield [54].

Ultrafast non-radiative decay of a thermalized distribution ofexcitons, as observed in the above-mentioned studies, is consis-


tent with the low quantum yield measured through steady-statephotoluminescence spectroscopy. The role of defect and surfacetraps on exciton recombination has been explored through life-time measurements as a function of the TMD layer thickness.Using ultrafast differential transmission spectroscopy, Wang etal. demonstrate that the exciton lifetime increases from a fewtens of picoseconds for a single monolayer to a nanosecond for10 layers in exfoliated MoS2 at room temperature. This behavioris attributed to a short defect-assisted recombination lifetimefor the surface layers in a few-layer sample and a long recombi-nation lifetime for all the inner layers. The effective lifetime isestimated by taking into account the probability of electron andhole occupation in each layer using the effective mass approxi-mation. The short exciton lifetime in the monolayer is attributedto fast defect-assisted carrier recombination via Auger scatter-ing, which decreases in probability as the sample thickness is in-creased [35]. Similar surface-recombination dynamics have beenobserved in more conventional semiconductor nanostructures,which have benefitted from passivation schemes that reduce thenumber of available non-radiative recombination sites [55, 56].In monolayer TMDs, specifically exfoliated MoS2, treatmentswith a non-oxidizing organic superacid, bis(trifluoromethane)sulfonimide (TFSI), increase the exciton lifetime measured atroom temperature from 100 ps to more than 10 ns and enhancethe quantum yield by more than two orders of magnitude–upto 95%. [32]. This air-stable, solution-based passivation processpoints toward a systematic method for minimizing contributionsto exciton recombination dynamics from defects and impurities.

3. COHERENT DYNAMICS

While time-resolved photoluminescence and pump-probe tech-niques provide essential information regarding exciton radiativeand non-radiative recombination (T1 dynamics), they do not pro-vide any details of the exciton coherent dynamics. The excitoncoherence time (T2)–which reflects the timescale during which asuperposition of the crystal ground and excited exciton statesevolves with a fixed phase relationship–is a fundamental param-eter of light-matter interaction in semiconductors (see Fig. 6(a)).In principle, T1 and T2 reflect the fundamental timescales forcoherent opto-electronic, photonic, and quantum informationapplications. The coherence time can be probed in either thetime or frequency domains; however impurities and defects giverise to local potentials that shift the exciton transition, resultingin an inhomogeneous distribution of exciton frequencies. Insteady-state photoluminescence spectra, the exciton linewidth isa convolution of the intrinsic homogeneous linewidth (inverselyproportional to T2) and the inhomogeneous linewidth, whichtypically dominates the optical spectra as shown in Fig. 6(b).

To separate exciton homogeneous broadening from inhomo-geneous broadening in TMDs, optical two-dimensional coherentspectroscopy (2DCS) has been employed, which is a three-pulsefour-wave mixing (photon echo) technique [31]. In this study, aseries of 100-fs laser pulses with phase-stabilized, variable delayscoherently interact with a monolayer WSe2 sample grown viachemical vapor deposition on a sapphire substrate. The coher-ent light-matter interaction generates a third-order polarizationthat is radiated as a photon echo, which is detected throughheterodyne spectral interferometry. A two-dimensional Fouriertransform of the four-wave mixing signal with respect to the var-ied delays generates a two-dimensional spectrum that correlatesthe excitation and emission energies of the system, shown in Fig.6(c). The spectrum features a single peak centered at the exciton

absorption energy. The linewidth along the diagonal dashedline reflects the amount of inhomogeneous broadening in thematerial, whereas the half-width at half-maximum of the cross-diagonal lineshape provides a measure of the homogeneouslinewidth (γ), as shown in Fig. 6(d) [57].


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Fig. 6. (a) The coherent quantum dynamics of an exciton withresonance frequency ω0 are characterized by the recombina-tion rate Γ (lifetime T1 = h̄/Γ) and homogeneous linewidthγ (coherence time T2 = h̄/γ). The two are related throughγ = Γ/2 + γ∗, where γ∗ is the pure dephasing rate de-scribing elastic processes that interrupt the phase coherencewithout affecting the excited-state occupation. (b) Inhomoge-neous broadening (Γin) due to a varying local potential resultsin a distribution of exciton transition frequencies. (c) Two-dimensional coherent spectrum of the exciton transition at 5K. The linewidth along the diagonal dashed line provides ameasure of the inhomogeneous linewidth, whereas the half-width at half-maximum along the cross-diagonal line providesthe homogeneous linewidth. (d) A cross-diagonal slice takenat the maximum amplitude of the spectrum in (c) is fit witha square root of Lorentzian function to yield γ = 2.7 meVat an excitation density of 1011 cm−2. (e) The homogeneouslinewidth increases linearly with exciton density up to ∼ 1012

cm−2, shown for 10 K. (f) The extrapolated zero-density homo-geneous linewidth as a function of temperature. Data repro-duced from [31].

The narrow homogeneous linewidth, on the order of a fewmeV, compared to the ∼ 50 meV inhomogeneous linewidth,confirms the presence of varying local potentials via defectsand impurities in this particular study. Weak localization lead-ing to inhomogeneous broadening of the exciton resonance isalso observed in exfoliated monolayer samples, which resultsin the appearance of an exciton “mobility edge” separating “lo-calized” and “delocalized” states within the exciton transition


[27]. While the exciton lifetime is independent of the excitationdensity below 1012 cm−2 as discussed in the previous section,the homogeneous linewidth increases linearly with density asshown in Fig. 6(e). This behavior is reminiscent of excitonexcitation-induced dephasing in conventional semiconductorsthat arises from elastic scattering of excitons [58]. Interestingly,the amount of exciton-exciton interaction broadening in TMDsis nearly an order of magnitude larger than traditional semicon-ductor nanostructures, which is attributed to reduced dielectricscreening of the Coulomb interaction in TMDs.

1.62 1.63 1.64 1.65 1.66 1.67

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Fig. 7. (a) Degenerate differential reflectance (dR/R) spec-trum from exfoliated monolayer MoSe2 taken at 30 K featur-ing the exciton and trion resonances near 1.66 and 1.63 eV,respectively. The peak assignments are consistent with thelow temperature photoluminescence spectrum (inset). Thecolored arrows indicate the spectral position of the pump inthe non-degenerate spectra. (b)-(d) Non-degenerate differen-tial reflectance spectra as a function of pump energy tunedthroughout the exciton resonance for cross-linearly polarizedpump and probe. The linewidth extracted from the real andimaginary components of a complex Lorentzian fit functionare shown in (e). The linewidth full-width at half-maximum(FWHM) increases linearly with the pump power. Data repro-duced from [59].

The role of acoustic phonons in exciton dephasing is reflectedin the temperature dependence of the homogeneous linewidth.At each temperature, the excitation density dependence of thelinewidth is measured. The extrapolated zero-density linewidthsare shown in Fig. 6(f) for temperatures up to 50 K. The residualhomogeneous linewidth extrapolated to zero density and zero

temperature is γ = 1.6 meV. This value is limited only by theexciton recombination lifetime in this study (a few hundredfemtoseconds), obtained from a variation of 2D spectroscopythat is equivalent to optical pump-probe techniques. This is aninteresting result, since it implies that the fast radiative and non-radiative recombination dynamics leading to the sub-picosecondexciton lifetime do not introduce additional pure dephasing inthis sample, i.e. γ∗ = 0.

Additional insight into the coherent quantum dynamics ofexcitonic transitions in monolayer TMDs is provided throughultra high-resolution differential reflectance (DR) spectroscopy.In this study, the authors perform a two-color continuous-wavepump-probe experiment on monolayer MoSe2 exfoliated ontoan SiO2/Si substrate at 30 K [59]. A pump laser is resonant withthe exciton resonance while a probe laser is scanned throughzero pump-probe detuning. Through modulation of the pumpand probe amplitudes and lock-in detection referenced to thedifference in modulation frequencies, the technique is sensitiveto ultra-narrow resonances corresponding to ultra-long decaydynamics. A degenerate DR spectrum obtained by scanning thepump and probe frequencies for zero pump-probe detuning isshown in Fig. 7(a), which is used to characterize the sample.Comparing the DR nonlinear optical response to the photolumi-nescence spectrum (inset in Fig. 7(a)), the two resonances areattributed to the exciton and trion transitions at 1.655 and 1.625eV, respectively.

In contrast to the few-meV linewidth of the exciton resonancein the degenerate DR spectrum, the high-resolution two-colorDR measurements feature µeV-wide resonances superimposedonto an meV-wide background that closely resembles the de-generate DR spectrum. Two-color DR spectra are shown inFig. 7(b)-7(d) for cross-linearly polarized pump and probe fieldsat three different pump energies. Each spectrum is fit with acomplex Lorentzian function to extract a linewidth. A powerdependence of the linewidth is shown in Fig. 7(e) for the pumptuned to the peak of the exciton resonance in the degenerateDR spectrum (corresponding to the lineshape in Fig. 7(d)). Ex-trapolating to zero pump power reveals a linewidth of ∼ 1.5µeV.

Both spectral-hole burning and coherent population oscil-lation nonlinearities contribute to the measured linewidths inFig. 7. The few-meV wide background on the lineshapes isattributed to spectral hole burning, which provides a measure ofhomogeneous and inhomogeneous broadening. The µeV widthis associated with coherent population oscillations that reflecta long-lived (nanosecond) component. Using a model basedon the optical Bloch equations for a 5-level system, the authorsattribute the long lifetime to a combination of both bright anddark exciton transitions that includes non-radiative decay to along-lived state as well as inter-valley scattering. The pumpfluence dependence of the linewidth shown in Fig. 7(e) points tothe influence of interaction effects such as exciton-exciton Augerrecombination. Using co-circular polarization of the pump andprobe fields, an additional sub-µeV component correspondingto nearly a 10 ns lifetime appears, indicating the presence ofan additional long-lived state. Understanding the origin of thisstate might help explain the fast exciton recombination and lowquantum yield at low temperature and the increase in excitonlifetime at elevated temperature in some experiments.


4. VALLEY POLARIZATION AND VALLEY COHERENCEDYNAMICS

The bright exciton spin and valley relaxation dynamics can bemodeled within a pseudospin formalism (see [41] for a review).The pseudospin (S) components describe the orientation of themicroscopic exciton dipole moment: Sz gives the degree towhich excitons remain in their initial K/K′ valley (valley po-larization), whereas Sx and Sy give the degree of linear polar-ization corresponding to a coherent superposition of excitons inboth K and K′ valleys (valley coherence). Enhanced Coulombinteractions in monolayer TMDs lead to exciton spin and val-ley depolarization through the long-range exchange interaction.The pseudospin formalism readily takes into account intra- andinter-valley exchange effects [60–62], the latter of which acts asan effective magnetic field that induces coupling between the Kand K′ valleys.

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Fig. 8. Circularly polarized time-resolved photoluminescenceintensity of the exciton resonance from exfoliated monolayerMoS2 at (a) 4 K and (b) 300 K (left axes). The excitation laser isσ+ circularly polarized. Right axes: Degree of circular polar-ization during the exciton emission. Lowering the laser powerby two orders of magnitude increases the degree of polariza-tion, indicated by the red data points in (a). Data reproducedfrom [63].

This formalism has been successfully applied to model theexciton spin and valley depolarization dynamics measured us-ing time-resolved photoluminescence [61] and Kerr rotationspectroscopies [46]. The role that the long-range exchange inter-action plays in inter-valley depolarization has also been identi-fied through a combination of time-resolved and polarization-resolved photoluminescence [63, 64] and transient absorption[65] spectroscopy studies. Figure 8 shows polarization- and time-resolved photoluminescence from monolayer MoS2 exfoliatedonto a 90-nm-thick SiO2/Si substrate at two different tempera-tures (left axes) [63]. Non-resonant σ+ polarized excitation is

used and both σ+ and σ− components (solid and dashed lines,respectively) of the emission are detected at the lowest energyexciton resonance. Exciton recombination occurs within 4 ps atboth 4 K and 300 K.

The degree of circular polarization is nearly constant for theentire duration of emission (blue data points in Figs. 8(a) and8(b), right axes). As the excitation fluence is reduced by two or-ders of magnitude, the degree of circular polarization increasesfrom ∼ 50% to ∼ 60% at 4 K. Given the measured exciton life-time, which includes contributions from both radiative and non-radiative recombination, and assuming an initial valley polar-ization of 100%, the extracted valley lifetime is 7 ps. Similartimescales are also observed in exfoliated WSe2 [66]. Fast valleydepolarization is consistent with theoretical estimates using thepseudospin formalism [41]. The exciton spin and valley depolar-ization time has also been predicted to decrease with increasingtemperature due to the long-range exchange interaction, whichagrees well with Kerr rotation experiments [46]. Despite fastspin and valley relaxation, the degree of circular polarization asmeasured in steady-state photoluminescence experiments canbe near 100% owing to exciton recombination typically occur-ring on the same ultrafast timescale. Using circularly polarizedtransient absorption spectroscopy, a longer valley lifetime com-ponent on the order of 100 ps has been measured, which isattributed to two processes: direct scattering of the exciton fromthe K to K′ valley accompanied by a spin flip, and scattering ofthe exciton through a spin-degenerate Γ valley [45].

The electron-hole exchange interaction also plays an impor-tant role in exciton valley coherence. In steady-state photolu-minescence spectra, valley coherence is identified through theobservation of linearly polarized emission oriented parallel tothe linearly polarized excitation field [17, 19]. The σ+ and σ−polarized components of the excitation field generate hot car-riers in both the K and K′ bands, which subsequently cool toform a thermal distribution of excitons that eventually recom-bines. The initial phase relationship of the circularly polarizedcomponents of the excitation field is maintained during thisprocess, resulting in linearly polarized emission. In these initialstudies, a degree of linear polarization close to 50% is reported,which decreases as the excitation energy increases above theexciton resonance energy. Such a behavior points to contribu-tions from the electron-hole exchange interaction on the valleycoherence dynamics. To probe these effects, the valley coher-ence time has been measured using two-dimensional coherentspectroscopy [67]. In this work, the authors resonantly generatevalley coherence in WSe2 using a series of circularly polarizedlaser pulses, analogous to a stimulated Raman-type process.The non-radiative valley coherence is converted to an opticalcoherence in the K′ valley that is detected through spectral inter-ferometry. The delay between the laser pulses is varied to mapout the valley coherence, which exponentially decays on a sub-picosecond timescale. A model based on the Maialle-Silva-Shammechanism reproduces the measured valley dynamics [68, 69],highlighting the role of both exciton population recombinationand electron-hole exchange in exciton valley decoherence.

5. OUTLOOK

The understanding of exciton recombination and decoherencedynamics has rapidly progressed since the seminal works iden-tifying monolayer TMDs [4, 5]. Although research of monolayerTMDs only began in the last decade, the breadth of experimentaland theoretical studies have elucidated many important pro-


Table 1. Exciton Recombination Lifetime and Coherence Time in Monolayer TMDs

Material (Temp.) Recombination (T1) and Coherence (T2) Times Reference

WSe2 (300 K) T1,fast = 150 fs Poellmann et al. [30]

WSe2 (Various) T1,fast = 210 fs (10 K); T1,slow = 17 ps (10 K); T2 = 150− 410 fs (50-0 K) Moody et al. [31]

WSe2 (Various) T1,fast ≤ 10 ps (≤ 80 K); T1,slow ≈ 1 ns (290 K) Zhang et al. [43]

WSe2 (300 K) T1 = 18 ps Cui et al. [47]

WSe2 (300 K) T1 ≤ 100 ps (12 µJ/cm2); T1 ≈ 4 ns (0.006 µJ/cm2) Mouri et al. [53]

WSe2 (4 K) T1,fast ≤ 4 ps; T1,slow = 33 ps Wang et al. [66]

MoS2 (300 K) T1 = 300 ps (untreated); T1 = 10.8 ns (passivated) Amani et al. [32]

MoS2 (300 K) T1 = 50 ps Wang et al. [35]

MoS2 (Various) T1,fast = 5 ps (5 K); T1,slow ≈ 100 ps (270 K) Korn et al. [39]

MoS2 (300 K, susp.) T1,fast = 2.6 ps; T1,mid = 74 ps; T1,slow = 850 ps Shi et al. [40]

MoS2 (300 K, supp.) T1,fast = 3.3 ps; T1,mid = 55 ps; T1,slow = 469 ps Shi et al. [40]

MoS2 (300 K) T1 = 19 ps (22 µJ/cm2); T1 ≈ 360 ps (3 µJ/cm2) Sun et al. [49]

MoS2 (4 K) T1 = 4 ps Lagarde et al. [63]

MoSe2 (4 K) T1 ≤ 3 ps Wang et al. [42]

MoSe2 (30 K) T1,fast = 1.7 ns; T1,slow ≈ 6 ns Schaibley et al. [59]

cesses that govern exciton dynamics. Specifically, exciton ther-malization has been identified as one leading factor dictatingthe recombination timescale. At room temperature, a thermaldistribution of excitons in momentum space leads to an effectiveradiative lifetime on the order of 100 ps to 1 ns. At cryogenictemperatures, the extent of the distribution is reduced, resultingin a sub- to few-picosecond effective lifetime. Non-radiative re-combination through Auger-type scattering and defect-assistedrelaxation channels compete on a similar timescale. These contri-butions can be minimized using low pump fluence and surface-state passivation treatments, respectively, which extend the effec-tive radiative lifetime to nearly 11 ns and enhance the quantumyield to ∼ 95% at room temperature. The presence of low-lyingdark states appearing through intra- and inter-valley spin scat-tering can also lead to an additional fast relaxation channel atlow temperature. In Table 1, we provide an overview of theexciton recombination and decoherence timescales reported inthe literature to date.

Minimizing non-radiative recombination in monolayerTMDs is a highly sought goal that would enable novel high-performance opto-electronics and photonics applications. Fu-ture studies of exciton dynamics in monolayer TMDs may yieldfurther insight by combining several of the techniques and con-trol knobs discussed in this review into a single experiment. Forexample, time-resolved photoluminescence and Kerr rotationspectroscopy experiments on passivated samples, performed atvarious temperatures, may reveal longer exciton lifetimes thatare compatible with electronically accessible (≥ nanosecond)time scales. Combined with coherent nonlinear spectroscopyexperiments, the full exciton quantum dynamics including pop-ulation recombination and decoherence times could be character-ized. Novel quantum phenomena and optoelectronic propertiesmight be revealed by applying similar techniques to study otherexciton-type states including charged and multi-excitons, local-

ized quantum dot-like excitons [70–73], indirect excitons in bilay-ers [74, 75] and heterostructures [76, 77], and exciton-polaritons[78].

FUNDING INFORMATION

J.S. and X.X. are supported by the Department of Energy, Ba-sic Energy Sciences, Materials Sciences and Engineering Divi-sion (DE-SC0008145 and DE-SC0012509) and AFOSR (FA9550-14-1-0277). X.X. thanks support from Cottrell Scholar Awardand support from the State of Washington funded Clean En-ergy Institute.

ACKNOWLEDGMENTS

The authors thank Tobias Korn, Bernhard Urbaszek, and HuiZhao for providing experimental data for this article.

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